Question: Solve for $x$ and $y$ using substitution. ${-3x-6y = 3}$ ${y = 3x-4}$
Since $y$ has already been solved for, substitute $3x-4$ for $y$ in the first equation. ${-3x - 6}{(3x-4)}{= 3}$ Simplify and solve for $x$ $-3x-18x + 24 = 3$ $-21x+24 = 3$ $-21x+24{-24} = 3{-24}$ $-21x = -21$ $\dfrac{-21x}{{-21}} = \dfrac{-21}{{-21}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = 3x-4}\thinspace$ to find $y$ ${y = 3}{(1)}{ - 4}$ $y = 3 - 4$ $y = -1$ You can also plug ${x = 1}$ into $\thinspace {-3x-6y = 3}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ - 6y = 3}$ ${y = -1}$